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d_7^2+d_{15}^2=d_{16}^2, d_{17}=?

Source: India tst 2006 p8

June 26, 2012
number theory proposednumber theory

Problem Statement

the positive divisors d1,d2,⋯ ,dkd_1,d_2,\cdots,d_k of a positive integer nn are ordered 1=d1<d2<⋯<dk=n1=d_1<d_2<\cdots<d_k=n Suppose d72+d152=d162d_7^2+d_{15}^2=d_{16}^2. Find all possible values of d17d_{17}.
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